摘要
本文借助双线性元积分恒等式技巧,对粘弹性方程的类Wilson元解进行了高精度分析.通过证明类 Wilson元的非协调误差在矩形网格下可以达到O(h3)这一独特性质及利用插值后处理技术给出了H1模意义下O(h2)阶的超逼近和整体超收敛结果.进而通过构造合适的外推格式,得到具有更高阶O(h3)精度的数值逼近解.
In this paper,based on the integral identities technique of the bilinear element, higher accuracy analysis of quasi-Wilson element is discussed for the viscoelasticity type e- quations. Moreover,lt is proved that special character of the nonconforming error of quasi- Wilson element is of order O（h3） under rectangular meshes, which leads to the superclose property of order O（hz） and the global supereonvergence result in broken H1 -norm by use of interpolated post-processing method. The numerical approximation solution with higher accu- racy of order O（h＂3） is derived through constructing a proper extrapolation scheme.
出处
《应用数学》
CSCD
北大核心
2012年第2期396-402,共7页
Mathematica Applicata
基金
国家自然科学基金(10671184
10971203)
国家自然科学基金数学天元基金(11026154)
高等学校博士学科点专项科研基金(20094101110006)
河南省教育厅自然科学基金(2010A110018)
关键词
粘弹性方程
类WILSON元
高精度分析
超收敛及外推
Viscoelasticity type equations
Quasi-Wilson element
Higher accuracy analysis
Superconvergence and extrapolation
